With his spiky gray hair and the top few buttons of his shirt undone, Jann S. Wenner looked every bit the aging but still vigorous lion of pop-culture media as he sat in his cavernous Manhattan office last week, editing by pen and paper a coffee-table book for Rolling Stone’s 50th anniversary next year.

Around the corner, in a much smaller office, was Mr. Wenner’s 26-year-old son, Gus, who as head of digital is charged with leading the family business into the future.

Together they are trying to steer the business, Wenner Media, through perhaps the strongest headwinds in its history, as the market for print magazines erodes, the company works to pay off debt and an $8 million defamation trial opens on Monday in a federal court in Virginia — the first of two lawsuits that Rolling Stone faces over a discredited 2014 article about an alleged gang rape at the University of Virginia.

The article, which the magazine retracted after its flaws were dissected in a Columbia Journalism School report, brought Rolling Stone its widest but most unwelcome attention in years. And the suits are the latest example of a media outlet defending itself in a high-profile court case, after Gawker Media was sued by Terry Bollea, the former professional wrestler known as Hulk Hogan, for invasion of privacy, a case that resulted in $140 million in damages and forced Gawker into bankruptcy.

In this first case, Rolling Stone faces a University of Virginia associate dean who says she was smeared by the article; a second, filed in a Virginia state court by the fraternity that was portrayed as the setting for the alleged gang rape, seeks $25 million in damages and has not yet gone to trial. Legal experts say that even if Rolling Stone loses, it is unlikely to suffer the same fate as Gawker, and Jann Wenner, 70, said that his company — which also publishes US Weekly and Men’s Journal — was well covered by insurance.

The elder Mr. Wenner, who helped found Rolling Stone as a 21-year-old college dropout in San Francisco and is its editor, was also adamant that the magazine’s reputation would survive, pointing to its history of journalistic coups and its legacy as a home to literary icons like Hunter S. Thompson and Tom Wolfe.

“Our journalistic reputation is shining,” Mr. Wenner said in an interview.

Others are not so convinced. Once holding an unparalleled influence over pop culture, Rolling Stone has long been criticized as being too in thrall to rock’s graying heroes; the current issue features Bruce Springsteen on the cover. The magazine received attention in January when it published a popular, but also criticized, exclusive interview with the notorious Mexican drug kingpin known as El Chapo.

William McKeen, a journalism professor at Boston University who has written a biography of Thompson, called the failures of the Virginia story “devastating” and said that the fallout from it “offsets, maybe in this case, generations of good writing.”

In some ways, the Virginia controversy could not have come at a worse time for Wenner Media. Like other magazine publishers, it has struggled to find new sources of income to make up for a fading print business, and gone through painful cost-cutting. Wenner’s three magazines had $330 million in revenue for the year that ended in June, down from $354 million the year before, according to Moody’s Investors Service.

Wenner, which is privately owned, also shoulders more than $14 million in debt payments each year for a loan that dates to 2006, when the company borrowed $300 million to buy back the 50 percent share in US Weekly that it had sold to Disney for $40 million just five years before. Analysts say that Wenner has been disciplined in paying down the loan — its obligation is now $59 million — but described the terms as aggressive, since lenders want to make their money back before the magazine business falls apart.

Last month, in a $40 million deal, Wenner Media sold a 49 percent stake in Rolling Stone to BandLab Technologies, a Singapore-based music tech company. Wenner used $25 million from that transaction for a special payment on its loan, according to credit reports, and the rest is intended as an investment to expand Rolling Stone’s reach internationally, and into new areas of branding and licensing like concerts and hotels.

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The article at the center of two defamation trials against Rolling Stone.

The Singapore deal was a coming-out of sorts for Gus Wenner, who was appointed to his current position two years ago and has quickly become the company’s heir apparent. For years, Jann Wenner had seemingly never needed a succession plan.

“Some people are 60 going on 70,” said Janice Min, the chief creative officer of The Hollywood Reporter and a former editor of US Weekly. “Jann was 60 going on 40.”

Gus Wenner’s duties include broad oversight of online business and editorial content for all Wenner publications. In an interview, he described priorities like video, licensing and brand partnerships.

“Maybe some of it was intuitive,” said the younger Mr. Wenner, “but I don’t think you have to be a genius to look at where certain trends are going in the business.”

His quick rise has drawn plenty of sniping in media circles about nepotism. But Mr. Wenner has also earned a grudging respect for his pursuit of new business deals, which have included a partnership with Google for Rolling Stone’s cover archive. The site has also grown, with an average of 17 million unique visits so far this year, up about 90 percent from the same period in 2014, according to comScore. Rolling Stone says that 47 percent of its advertising revenue is now digital.

“To his credit,” Matt Mastrangelo, a former publisher of Rolling Stone, said of Gus, “he has been able to get Jann to understand that if the company is going to have a chance in this fractured, crazy media landscape, they have to go all-in on digital.”

When asked how he was able to make the changes, Gus Wenner said, “I had a very clear line to my dad.”

The company’s most immediate concern is the lawsuit in Virginia, which was filed by Nicole P. Eramo, the associate dean. In court filings, her lawyers assert that Rolling Stone and the author of the article, Sabrina Rubin Erdely — also a defendant in the cases — were reckless in their reporting and editing, and that Ms. Erdely deliberately avoided following leads that could have disproved the story.

Rolling Stone said that its source for an account of a rape, a student identified only as Jackie, had been introduced to the reporter by a university employee, and that its portrayal of Ms. Eramo and the administration was supported by a report by the United States Department of Education that criticized the university’s handling of sexual assault cases.

Legal experts following the case said that neither side had a clear advantage. Rolling Stone faces a hometown jury and the fact that it has already disavowed the article. But since Ms. Eramo was deemed by the judge to be a public figure, she must meet a difficult standard of proving actual malice, meaning that Rolling Stone knew or must have known that its article was false before publication.

“The Columbia Journalism School condemned Rolling Stone,” Elizabeth M. Locke, a lawyer for Ms. Eramo, said in a statement, “and we are confident that a jury will do so as well.”

Jann and Gus Wenner declined to comment on the litigation. But just days before the trial was to begin, Gus Wenner sounded optimistic about the magazine’s future.

“It is certainly a transformational moment for the company, and it will not be easy,” he said. “But we have made some important moves to set ourselves up for success, and I could not be more excited.”